Symmetries and overparametrization properties of Hamiltonian variational ansatzes for the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory

• URL: http://arxiv.org/abs/2606.05719v1
• Date: Thu, 04 Jun 2026 05:23:17 GMT
• Title: Symmetries and overparametrization properties of Hamiltonian variational ansatzes for the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory
• Abstract summary: We study five Hamiltonian variational ansatzes based on the Hamiltonian of the $(1+1)$dmathbbZ$ lattice gauge theory.<n>The ansatzes are designed to respect local and global symmetries of the original Hamiltonian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We perform detailed studies of five Hamiltonian variational ansatzes (HVA) based on the Hamiltonian of the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory. The ansatzes are designed to respect local and global symmetries of the original Hamiltonian and therefore act on a finely segmented state Hilbert space. Following Larocca et al. (2023), we numerically study the dimension of the dynamical Lie algebra (DLA) and the rank of the quantum Fisher information matrix (QFIM) of the ansatzes within specific invariant subspaces. The ansatzes all involve sums of weight-three Paulis in their generators, which is a feature that have so far been underexplored in this context. We also perform numerical experiments to determine the ground state energy of the original Hamiltonian via variational quantum eigensolver (VQE), and observe that overparametrization of the ansatzes coincides with the apparent disappearance of local minima in the loss function, in line with the finding in the reference. Finally, the decay rate of the VQE loss function under gradient descent optimization is revealed to scale linearly with the number of parameters in the ansatz. These results help to enrich the theory of overparameterization of quantum circuits and inform the design of scalable variational ansatzes.

Related papers

• Neural quantum states for non-Abelian lattice gauge theories with dynamical fermions [0.0028001975341488856]
  Ground state of non-Abelian lattice gauge theories coupled to dynamical fermions is key to understanding confinement.<n>We present a variational Monte Carlo framework for the ground state of the untruncated fully-continuous SU$(2)$ lattice gauge theory.<n>More broadly, the framework offers a sign-problem-free variational framework for continuous non-Abelian gauge groups with dynamical matter.
  arXiv  Detail & Related papers  (2026-07-28T18:00:01Z)
• Deforming the Trail: Baseline Quantum Circuitry for $\text{SU(2)}_k$ Lattice Gauge Theory [0.0]
  We provide a strategy of gauge-variant completions to extend unitarity to the entire computational Hilbert space.<n>We show that the physical Hilbert space dimension of the deformed plaquette operator scales equivalently to its non-deformed counterpart with a constant factor.<n>Q-deformation continues to pass scrutiny as a reliable truncation offering advantages in quantum circuit synthesis.
  arXiv  Detail & Related papers  (2026-05-14T17:01:35Z)
• Typical entanglement in anyon chains: Page curves beyond Lie group symmetries [41.99844472131922]
  We study bipartite entanglement statistics in one-dimensional anyon chains constrained by fusion rules of unitary pre-modular categories.<n>Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(sqrtL)$ or $O(1)$ symmetry-type corrections.<n> Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions.
  arXiv  Detail & Related papers  (2026-03-26T18:00:03Z)
• Optimal local basis truncation of lattice quantum many-body systems [0.0]
  We show how to optimally reduce the local basis of lattice quantum many-body (QMB) Hamiltonians.<n>The basis truncation exploits the most relevant eigenvalues of the estimated single-site reduced density matrix.
  arXiv  Detail & Related papers  (2025-09-22T16:22:54Z)
• Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow [44.500314182711236]
  We derive explicit ordinary equations govern the evolution of mean, covariance, and mass under HK-Boltzmann flow.<n>We demonstrate exponential convergence to equilibrium through constructing a gradient structure associated with a Polyak-Lojasiewicz-type inequalities.<n>We extend our analysis to non-Gaussian targets exhibiting strong log-lambda-concavity.
  arXiv  Detail & Related papers  (2025-04-29T03:54:56Z)
• Towards the phase diagram of fermions coupled with $SO(3)$ quantum links in $(2+1)$-D [0.0]
  Quantum link models (QLMs) are generalizations of Wilson's lattice gauge theory formulated with finite-dimensional link Hilbert spaces.<n>We extend the model to $(2+1)d$ dimensions for the first time, and report on our initial results.
  arXiv  Detail & Related papers  (2024-12-12T19:13:05Z)
• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories [40.772310187078475]
  We propose a novel variational ansatz for the ground-state preparation of the $mathbbZ$ lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve $>!99%$ precision in energy in both the confined and deconfined phase of the $mathbbZ$ LGT.
  arXiv  Detail & Related papers  (2023-08-07T14:23:00Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Distorted stability pattern and chaotic features for quantized prey-predator-like dynamics [0.0]
  Non-equilibrium and instability features of prey-predator-like systems are investigated in the framework of the Weyl-Wigner quantum mechanics. From the non-Liouvillian pattern driven by the associated Wigner currents, hyperbolic equilibrium and stability parameters are shown to be affected by quantum distortions.
  arXiv  Detail & Related papers  (2023-03-16T19:55:36Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Spectral Analysis of Product Formulas for Quantum Simulation [0.0]
  We show that the Trotter step size needed to estimate an energy eigenvalue within precision can be improved in scaling from $epsilon$ to $epsilon1/2$ for a large class of systems. Results partially generalize to diabatic processes, which remain in a narrow energy band separated from the rest of the spectrum by a gap.
  arXiv  Detail & Related papers  (2021-02-25T03:17:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.